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FRM Part I · FRM Exam Part I · Measuring and Monitoring Volatility

After fitting a GARCH(1,1) model, an analyst wants to test whether it captures volatility clustering. Which diagnostic is most appropriate?

Test the squared standardized residuals with a Ljung-Box test. If the GARCH model is adequate, no significant autocorrelation should remain in them, showing that volatility clustering has been captured.

  1. AApply a Ljung-Box test to the squared standardized residuals and look for no remaining autocorrelationCorrect
  2. BApply a Ljung-Box test to the raw returns and look for significant autocorrelation
  3. CCheck that the standardized residuals have a variance of exactly 2
  4. DCheck that omega exceeds alpha plus beta

Explanation

If the model captures volatility clustering, standardized residuals r_t/sigma_t should be roughly i.i.d., so their squares should show no significant autocorrelation under a Ljung-Box test. Raw-return autocorrelation tests mean dynamics, not variance dynamics. Standardized residuals should have variance near 1, not 2.

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